Use [tex]\log_e (1+x) \approx x - \frac{x^2}{2} + \frac{x^3}{3} [/tex] and let [tex] x = \sqrt{y} + \sqrt{1+y} -1 [/tex]. The first two terms of that expansion should clean up very nicely with the [itex]\sqrt{y}\sqrt{1+y}[/itex] from the original question, only slightly hard part is expanding that cubic term. Good luck